Delete Mesh by Material
To delete a part of a mesh by its material, you have at least two options.
For both to work you'll have to first enter edit mode (press Tab).
First option is to select by material. Here you can see where to find this command:

After running this command, you can press Del key, and select delete faces from popup menu.
Another option is to use separate by material. You can find it here (or press P in edit mode):

When you have separated part of your mesh into another object, you can do whatever you want to it, like delete it.